A350527 a(n) = c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).

0, 4, 5, 14, 27, 30, 48, 52, 75, 102, 108, 140, 176, 184, 225, 234, 280, 330, 341, 396, 408, 468, 532, 546, 615, 688, 704, 782, 799, 882, 969, 988, 1080, 1176, 1197, 1298, 1320, 1426, 1536, 1560, 1675, 1700, 1820, 1944, 1971, 2100, 2233, 2262, 2400, 2430

Offset

1,2

Comments

The golden ratio r is the unique number x such that f(n*x)*c(n/x) - c(n*x)f(n/x) = n for all n >= 1.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = -n + A350526(n) = -n + f(n*x)*c(n/x), where f = floor, c = ceiling, and r = golden ratio.

Mathematica

r = GoldenRatio; c[x_] := Ceiling[x]; f[x_] := Floor[x];
Table[f[n r]*c[n/r], {n, 1, 100}] (* A350526 *)
Table[c[n r]*f[n/r], {n, 1, 100}] (* A350527 *)
Table[f[n r]*c[n/r] - c[n r]*f[n/r], {n, 1, 100}]  (* A000027 *)

Crossrefs

Cf. A001622, A350526.

Sequence in context: A006904 A200177 A241863 * A316415 A007084 A216243

Adjacent sequences: A350524 A350525 A350526 * A350528 A350529 A350530

Keyword

nonn

Author

Clark Kimberling, Jan 04 2022

Status

approved